System and method for reducing interference between satellites

ABSTRACT

A satellite system facilitates communications between earth stations and both geostationary satellites and non-geostationary satellites in an orbit at a lower altitude than that of said the geostationary satellites by preventing the non-geostationary satellite from transmitting signals that might possibly interfere with signals transmitted by the geostationary satellites. The non-geostationary satellite includes position acquisition subsystem for determining the position, and in particular the latitude, of the non-geostationary satellite relative to the surface of the earth. A data processor determines a forbidden band of locations on the surface of the earth all possible geostationary satellites and the non-geostationary satellite, at its determined position, are separated by less than a specified minimum discrimination angle. An antenna control subsystem in the non-geostationary satellite controls transmission of signal energy from the non-geostationary satellite in accordance with the satellites position so as to prevent transmission of signal energy from the non-geostationary satellite to said locations within the forbidden band.

The present invention relates generally to satellite communicationsystems, and particularly to methods and systems for reducing signalinterference between geostationary and non-geostationary satellitecommunication systems.

BACKGROUND OF THE INVENTION

The recent proliferation of satellite communication systems hasincreased the likelihood of interference between signals associated withneighboring satellites. Such interference can take place, for example,when a non-geostationary satellite comes within the field of view of ageostationary satellite. As is well known, geostationary satellitesremain fixed in equatorial orbits over particular locations on thesurface of the earth. Since geostationary satellites ordinarily exhibitsome minor variation in latitude relative to the equatorial arc, thereexists a narrow "geostationary band" centered about the equatorial arccorresponding to the set of orbital locations potentially occupied bygeostationary satellites. Unlike geostationary satellites, the orbits ofnon-geostationary satellites continuously vary with respect to theearth's surface. Non-geostationary satellites typically traverse low andmedium altitude orbits below the geostationary band.

Signal interference between geostationary and non-geostationarycommunication systems can result when non-geostationary satellites moveinto the field of view of ground stations oriented toward a particularsatellite within the geostationary band. The potential for suchinterference arises whenever a non-geostationary satellite becomeslocated proximate the feeder link path between a geostationary satelliteand one of its ground stations, hereinafter referred to as GSY groundstations. Such interference can occur because non-geostationarysatellite systems are generally allocated, on a secondary basis, thesame feeder link frequency bands primarily earmarked to geostationarysystems. Consequently, it is incumbent upon the operators ofnon-geostationary systems to avoid disrupting communication withingeostationary systems. Although it is conceivable that the feeder linkband could be shared by geostationary and non-geostationary systems, thefrequency separation required between the channels allocated to eachsystem in order to ensure acceptable interference levels would make thisapproach infeasible under most circumstances.

Since geostationary satellites are distributed throughout thegeostationary band above the surface of the equator, the points on thesurface of the earth in approximate alignment with the geostationaryband and a non-geostationary satellite form a range of "in-line"latitudes across the earth's surface. The position of this terrestrialin-line latitude range will vary with changes in the latitude of thenon-geostationary satellite. Yet non-geostationary satellites mayinterfere with geostationary systems even when not so aligned between ageostationary satellite and a GSY ground station, since the antenna ofthe GSY ground station projects a radiation pattern across a finitediscrimination angle relative to its beam axis. Accordingly, it hasgenerally been necessary for non-geosynchronous satellites to ceasesignal transmission when in orbit above GSY ground stations in thevicinity of this in-line latitude range. This restriction ontransmission range has hindered the performance of non-geostationarysatellite systems coordinated in frequency with geostationary systems.

One way of minimizing interference between geostationary andnon-geostationary systems would be simply to operate thenon-geosynchronous system over frequency bands not already allocated togeostationary systems. Unfortunately, the limited frequency spectrumavailable for satellite communication systems renders this solutionuntenable. Moreover, well-established technology is available forimplementing communications equipment designed to process signals overthe frequency bands primarily allocated to geosynchronous systems.

It is therefore an object of the present invention to provide a methodfor minimizing the potential for interference betweenfrequency-coordinated geostationary and non-geostationary satellitecommunication systems which does not require that non-geostationarysignal transmission be suspended from all non-geostationary orbitallocations in view of GSY ground stations.

SUMMARY OF THE INVENTION

In summary, the present invention is a method of facilitatingfrequency-sharing between a satellite system having a geostationaryorbital band occupied by at least one geostationary satellite and anon-geostationary satellite in an orbit at a lower altitude than that ofthe geostationary satellite. The method includes the steps of:determining the position of the non-geostationary satellite relative tothe surface of the earth; and calculating a minimum discrimination anglebetween the geostationary band and non-geostationary satellite at itsdetermined position relative to a ground station on earth. The minimumdiscrimination angle corresponds to a predefined threshold ofinterference between signals received by the ground station from thenon-geostationary satellite and geostationary satellites in thegeostationary orbital band. The method further includes the step ofdefining a forbidden band of locations on the surface of the earth fromwhich the geostationary orbital band and the non-geostationarysatellite, at its determined position, are separated by less than theminimum discrimination angle. The present invention enables interferenceto be minimized by limiting transmission of signal energy from thenon-geostationary satellite to regions outside of the forbidden band oflocations.

Alternately, the present invention can be viewed as the signaltransmission control apparatus for a non-geostationary satelliteoperating in conjunction with geostationary satellites.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional objects and features of the invention will be more readilyapparent from the following detailed description and appended claimswhen taken in conjunction with the drawings, in which:

FIG. 1 shows a geostationary satellite and a non-geostationary satellitein orbit above the earth's surface.

FIG. 2 illustratively represents the non-geostationary orbital pathfollowed by a conventionally-equipped non-geostationary satelliterelative to a geostationary satellite occupying an orbital location inthe geostationary band above the equator.

FIG. 3 shows a non-geostationary satellite NG' equipped with a forbiddenband antenna control system traversing a non-geostationary orbitaltrajectory NGO'.

FIG. 4 depicts the relationship of a non-geostationary satelliterelative to a geostationary satellite and to the earth.

FIG. 5 shows a block diagram of a forbidden band antenna control systemof the present invention designed for inclusion within anon-geostationary satellite.

FIG. 6 is a diagram depicting various geometrical relationships betweena geostationary satellite G and a non-geostationary satellite I relativeto the earth.

FIG. 7a shows an exact representation and an approximation of aforbidden band within the field of view of a non-geostationarysatellite.

FIG. 7b shows a projection of a forbidden band in the field of view of anon-geostationary satellite located at a particular orbital position.

FIG. 8a includes a representation on the earth's surface of thehorizontal approximation of the forbidden band shown in FIG. 7a.

FIG. 8b shows a representation of a set of forbidden bands on thesurface of the earth corresponding to various non-geostationary orbitalpositions.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Introduction

Referring to FIG. 1, there is shown a geostationary satellite 10 and anon-geostationary satellite 20 in orbit above the earth's surface 30.The geostationary orbital trajectory of the satellite 10 passesperpendicularly through the plane of FIG. 1, while the non-geostationarysatellite 20 may be assumed to be in a polar orbit transverse to thegeostationary band. The geostationary satellite 10 occupies a locationwithin the geostationary band above the equator Q, and hence remains ina fixed position relative to ground station 40. In the system shown inFIG. 1 the geostationary satellite 10 provides a communication link tothe ground station 40. The geostationary satellite 10 communicates withthe ground station 40 via antenna 60 over channels included within afeeder link band that may be simultaneously utilized by thenon-geostationary satellite 20.

As may be appreciated by reference to FIG. 1, the potential forinterference between the non-geostationary satellite 20 and thegeostationary satellite 10 arises when the non-geostationary satellite20 becomes located proximate the feeder link path (FP) between thegeostationary satellite 10 and the ground station 40. In accordance withthe invention, signals transmitted by the non-geostationary satellite 20are prevented from interfering, beyond a predefined extent, with signaltransmission between the geostationary satellite 10 and ground station40 by modifying the antenna beam pattern B radiated by thenon-geostationary satellite 20. As is described more fully below, thismodification involves nulling the portion of the beam pattern incidenton a "forbidden band" of latitudes (not shown to scale in FIG. 1) on thesurface of the earth. The forbidden latitude range corresponds to theset of locations from which the angular separation, i.e., topocentricangle, between satellite positions within the geostationary band and thenon-geostationary satellite is such that more than a minimum acceptablelevel of interference would exist between signals from the geostationaryand non-geostationary satellites 10 and 20 if beam pattern B from thenon-geostationary satellite 20 was not altered. The topocentric angularseparation corresponding to this minimum acceptable level ofinterference is derived below, and will be referred to hereinafter asthe minimum discrimination angle D_(min).

The manner in which the present invention allows a non-geostationarysatellite to remain operational even when in view of ground stations incommunication with geostationary satellites may be further appreciatedwith reference to FIGS. 2 and 3. FIG. 2 depicts a non-geostationaryorbital path NGO followed by a conventionally-equipped non-geostationarysatellite NG relative to an orbital location in the geostationary band,above the equator Q, of a geostationary satellite G. When the satelliteNG reaches orbital location A, the topocentric angular separationbetween the two satellites from surface location B is equal to theminimum discrimination angle. As the satellite NG traverses the orbitalpath NGO between orbital locations A and C, there will exist points onthe surface of the earth between locations B and D for which thetopocentric angle between the satellites is less than the minimumdiscrimination angle D_(min). This may be seen by observing that whenthe non-geostationary satellite NG occupies orbital positions betweenpoints E and F there exist locations between points B and D on thesurface of the earth from which the two satellites are in alignment,i.e., locations at which the topocentric angle is zero. It is furtherobserved that for non-geostationary orbital locations between positionsA and E, and between positions F and C, the corresponding topocentricangles at points B and D, respectively, are less than D_(min).

One way of guaranteeing that all ground stations between surfacelocations B and D experience less than the minimum acceptable level ofinterference would be to suspend transmission from the satellite NGwhile it is located between orbital positions A and C. The infeasibilityof this approach, however, may be demonstrated by considering thefollowing numerical example. Assuming a typical minimum discriminationangle D_(min) of 3 degrees, a ±3 degree latitude variation of thegeostationary satellite orbiting at a height of 35,786 km, and anon-geostationary orbit height of 1800 km, the non-geostationarysatellite would need to be switched off when between latitudesapproximately ±48 degrees from the equator. An interruption incommunication due to this switch-off could only be avoided if othersatellites having unused feeder link capacity were available to relaysignals from the non-geostationary satellite to its ground station. Asdescribed in the following section, a non-geostationary satellitedesigned in accordance with the invention to selectively communicateonly with locations not encompassed by a "forbidden band" of latitudesallows for substantially improved coverage range.

Overview of Forbidden Band Implementation

As shown in FIG. 3, a non-geostationary satellite NG' equipped with aforbidden band antenna control system is seen to follow anon-geostationary orbital trajectory NGO'. In accordance with theinvention, the antenna beam projected by the satellite NG' is directedonly to those regions on the surface of the earth from which thetopocentric angular separation between the satellite NG' and thegeostationary orbit exceeds the minimum discrimination angle D_(min). Inother words, for each latitude position on the orbital trajectory NGO'there exist locations on the earth between a forbidden band of latitudeswithin the field of view of the satellite NG' from which the topocentricangle is less than D_(min). The location of this forbidden band oflatitudes will shift as the satellite NG' traverses the orbitaltrajectory NGO'. In keeping with the invention, the antenna beamprojected by the satellite NG' is shaped so as to only transmit signalsto, and receive signals from, locations on the surface of the earth notcovered by the forbidden band.

As shown in FIG. 3, the forbidden band of latitudes corresponding to theindicated orientation of the non-geostationary satellite NG' relative toa geostationary satellite G' extends from latitude L1 to latitude L2about the equator Q. The forbidden band is positioned such that from thelatitudes L1 and L2 the topocentric angle between the satellites isequivalent to the minimum discrimination angle D_(min). It follows thatthe topocentric angle associated with locations within the forbiddenband is less than D_(min), while the topocentric angular separationbetween the satellites corresponding to locations outside of theforbidden band is larger than D_(min). In a preferred embodiment of theinvention the antenna beam pattern from the satellite NG' iscontinuously modified so as not to illuminate the forbidden bandcorresponding to the instantaneous latitude of the satellite NG'. Thismay be effected by, for example, selectively energizing a cluster ofspot beams projected by the antenna of the satellite NG' in accordancewith a switching algorithm. The switching algorithm will typically beresponsive to latitude information received from either the orbitcontrol system of the satellite or a ground station. In this regard amore detailed description of a forbidden band antenna control system isset forth in a following section.

Determination of the .Minimum Discrimination Angle D_(min)

Interference calculations are performed by separately consideringinterference between non-geostationary and geostationary downlink (i.e.,satellite to earth) and uplink (i.e., earth to satellite) frequencybands. That is, any interference between uplink and downlink bands isassumed to be of nominal magnitude relative to interference betweenbands of like type.

In a particular embodiment of the invention the value of the minimumdiscrimination angle, and hence the extent of the forbidden band,depends in part upon the signal to noise ratio required forcommunications carried by the feeder link between the geostationarysatellite 10 and ground station 40. Determination of the impact ofsignal transmissions from the non-geostationary satellite 20 upon thissignal to noise ratio will generally require knowledge of the frequencyand modulation characteristics of the feeder link, as well as ofspecific aspects of the communications hardware incorporated within thegeostationary and non-geostationary satellites 10 and 20 and within theground station 40, In this regard it will generally be necessary to beaware of the shape, or type, of the antenna beam B nominally projectedby the satellite 20, the gain of the antennas associated with the earthstation 40 and geostationary satellite 10, and the frequency (e.g.,C-Band, Ku-Band) and carrier characteristics (e.g., CDMA) of the feederlink.

Derivation of the Topocentric Angle η:

FIG. 4 is a diagram depicting the geometric relationship of anon-geostationary satellite S' relative to a geostationary satellite Sand to the earth. The angular separation between the geostationary andnon-geostationary satellites S and S' as seen from the center of theearth is denoted by α, while the separation between these satellites asseen from the location of a ground station on the surface of the earthis identified as the topocentric angle η. Given a particular value ofthe angle α between the two satellites, the corresponding topocentricangle η will vary in accordance with the location of the ground stationon the surface of the earth. It is assumed that the worst caseinterference situations arise when the topocentric angle is at a minimumfor a given geocentric angle α; that is, interference will be mostpronounced when the angular separation between the satellites is at aminimum when viewed from a ground station. Although the distancesbetween the ground station and the satellites vary as a function of thelatitude of the ground station, such variation is believed to have anegligible effect on interference levels relative to that arising as aconsequence of changes in the topocentric angle η.

Referring to FIG. 4, it may be seen that there exist geocentric anglesfor which the minimum topocentric angle, i.e., η_(min), is larger thanzero. This corresponds to the situation in which the satellites are notaligned from any location on the surface of the earth. Whether or notthe minimum topocentric angle η_(min) is nonzero will depend upon theorbit heights h and h' of the geostationary and non-geostationarysatellites relative to the surface of the earth. In particular, fororbit heights h and h' resulting in a geocentric angle α less than athreshold angle α_(min) there will exist ground station locationsrepresented by the vector E for which the minimum topocentric angleη_(min) is zero. Conversely, for satellite orbit configurations in whichα>α there exist ground station locations for which the associatedtopocentric angle η_(min) is not zero. The angle α_(min) may be derivedusing plane geometry, and is expressed below as: ##EQU1## where Ro isthe earth's radius, and h and h' are the respective orbit heights of thegeostationary and non-geostationary satellites S and S' (h>h'). Again,instances in which the geocentric angle is superior to the limit valueof equation (1) correspond to situations in which there are no groundstation locations aligned with the two satellites, i.e., η_(min) >0.

In what follows it is endeavored to determine an expression relating thelocation of a ground station to the topocentric angle η between thesatellites S and S' associated therewith. It is noted that the followingcalculations are referenced to the non-geostationary satellite S', as isindicated by the OXYZ coordinate system used in FIG. 4.

If Ro denotes the earth radius, and as previously mentioned h and h' theorbit heights of geosynchronous satellite S and non-geosynchronoussatellite S', respectively, wherein φ and θ are the sphericalcoordinates of ground station location E in the OXYZ coordinate system,one has: ##EQU2## Letting r and r' denote the ranges from ground stationlocation E to the satellites S and S', respectively, useful vectors aredefined by:

    ru=ES r'u'=ES'                                             (3)

so that the cosine of the topocentric angle is:

    cos .sub.η =u.u'                                       (4)

If one permits ground station location E to "move" on the surface of theearth while fixing the positions of satellites S and S', the opposite ofthe differential of E can be written:

    -dE=dru+rdu=dr'u'+r'du'                                    (5)

The calculation of the scalar product of this equation with the two unitvectors leads to: ##EQU3##

The differential of the cosine of the topocentric angle is then:##EQU4##

If θ is fixed, r' does not vary, so that one has: ##EQU5##

The term in brackets is positive, so that the cosine of the topocentricangle follows the variations of r and thus the variations of the squareof r, which is equal to:

    r.sup.2 =Ro.sup.2 +(Ro+h).sup.2 -2Ro(Ro+h)(cos θ cos α-sin θ sin α cos φ)                            (9)

Hence, when only φ varies, the cosine of the topocentric angle followsthe variations of the cosine of θ and therefore the topocentric angle,when θ is fixed, is minimum for φ=0.

In the rest of this section the geocentric angle is assumed to besufficiently low that there exist ground station positions correspondingto φ=0 in the field of view of satellite S. This condition can bewritten: ##EQU6##

It should be noted that this condition is not very restrictive since thelimit value, for a geostationary satellite S, is 81.3 degrees. Thefollowing notations are adopted for the rest of the section: ##EQU7##

With these notations, the conditions on α can be written:

    β-β'≦α≦β                (12)

The fact that the ground station location represented by the vector Emust be in the field of view of both satellites may be expressed usingequation (12) as:

    θ≦β-α                              (13)

Since the topocentric angle η is the difference between the elevation ofS' and the elevation of S as viewed from ground station location E, itis possible to represent the angle η as follows: ##EQU8## Thus, thetopocentric angle η decreases as the angle θ increases.

Forbidden Band Antenna Control System

Referring to FIG. 5, there is shown a block diagram of a forbidden bandantenna control system 100 of the present invention designed to beincluded within, for instance, the non-geostationary satellite NG'depicted in FIG. 3. Operation of the control system 100 is coordinatedby a central processing unit (CPU) 102, such as a microprocessor or thelike, on the basis of instructions received from a forbidden-bandantenna control program 104 stored within an on-board memory unit 108.The memory unit 108 further includes general purpose memory 112 and aforbidden-band look-up table 116.

The look-up table 116 contains information pertaining to the positionand shape of the forbidden band of locations on the surface of theearth. While in particular embodiments the forbidden band may beapproximated by a strip of surface locations included between a pair oflatitude boundaries, more accurate representations of the forbidden bandinclude latitude boundaries exhibiting a longitudinal dependence. Whenthe former approximation is employed the look-up table 116 will includepairs of forbidden band latitude boundaries L1 and L2 (FIG. 3) indexedas a function of the latitude of the non-geostationary satellite NG'. Itis anticipated that the look-up table would include boundaries of theforbidden latitude corresponding to a set of uniformly separatedlatitudes. An interpolation scheme could then be used to determineforbidden band boundaries corresponding to latitudes not included withinthe look-up table.

In order to approximate the forbidden band using latitude boundariesindependent of longitude, the entries within the look-up table 116 couldbe derived in a simplified manner, for example, by using the expressionfor topocentric angle given by equation (14) above. In an initial stepusing this approach the minimum discrimination angle D_(min) isdetermined as described in the preceding section. Followingdetermination of D_(min), computation of the topocentric anglescorresponding to a selected set of latitudes on the surface of the earthis generated for each satellite latitude index stored within the look-uptable 116. This step may be performed by, for example, substituting intoequation (14) a trial set of latitudes spanning a range believed toencompass the forbidden latitude band corresponding to the associatedsatellite latitude index. The topocentric angle corresponding to eachlatitude within the trial set is then compared with D_(min) in order todetermine the latitude boundaries L 1 and L2 of the forbidden band. Thatis, there will exist a pair of latitudes L1 and L2 within the trial setsuch that for all forbidden latitudes therebetween the associatedtopocentric angle will be less than D_(min). This description of asimplified technique for determining the boundaries of the forbiddenband is included at this juncture in order to enhance understanding ofthe control system 100. Accordingly, a more complete discussion of amethod for determining the limits of the forbidden band is detailed in asubsequent section.

Referring to FIG. 5, the antenna control system 100 also includes aposition acquisition subsystem 120 for supplying to the CPU 102information relating to the orbital location of the non-geostationarysatellite. The forbidden band antenna control program 104 uses the orbitlatitude provided by the subsystem 120 to retrieve the boundaries of theforbidden band from the look-up table 116. The CPU 102 then relays theretrieved forbidden band boundaries to an antenna control subsystem 124.The control subsystem 124 operates in a conventional manner to configurean antenna beam-forming network 128 used to drive the antenna 132 of thenon-geostationary satellite. The subsystem 124 controls the shape of thebeam pattern projected by the antenna by determining which of the feedelements within a feed array 136 are to be energized by the beam-formingnetwork 128. Electromagnetic energy is conventionally coupled from thebeam forming network 128 to the feed army 136 by waveguide 140, and isthen directed by the feed 136 to a doubly-curved shaped reflector 144.Although FIG. 5 depicts a particular system for projecting aforbidden-band beam pattern, other means within the scope of theinvention may be used to perform this function.

For example, in an alternate embodiment of the antenna control systemthe look-up table includes information relating to longitudinalvariation in the positions of the forbidden band boundaries. Such moreprecise forbidden band representations could each be stored, forexample, as a two-dimensional matrix associated with a particular orbitlatitude of the non-geostationary satellite. A set of mathematicalexpressions from which these two-dimensional forbidden bandrepresentations could be derived is set forth below. The geometricparameters included within the following expressions are defined withinthe diagram of FIG. 6, in which are shown various geometricalrelationships between a geostationary (GSO) satellite G andnon-geostationary (non-GSO) satellite l relative to the earth.

In another implementation of the antenna control system the look-uptable will include data corresponding to amplitude and phasecoefficients used in controlling individual elements within the antennafeed array. Such control data will generally be transmitted from aground station and stored within the look-up table prior to initiationof satellite operation. Since the orbit of non-geostationary satellitesis periodic, it is not required to generate a separate set of controldata based on recurring sets of geometrical satellite positionparameters. Although this approach may require a larger memory thanimplementations involving on-board generation of antenna controlsignals, it is simpler with regard to processing requirements and thelike. Moreover, in this approach control data corresponding torepresentations of the forbidden band exhibiting longitudinal variationcould be stored as easily as those in which the shape of the forbiddenband is specified simply by a pair of latitudes.

Geometrical Context of Forbidden Band Calculations

In what follows it is assumed that the position of the non-GSO satelliteis fixed at a given latitude, such that all calculations correspond to agiven instant in the non-GSO satellite orbital period. This allowslongitude to be determined relative to the non-GSO satellite. The GSOsatellite considered can have any longitude and a latitude between -3and +3 degrees, a range corresponding to the typical latitude drift ofGSO satellites. In all of the following calculations the variable ofinterest corresponds to the location of the ground station M on thesurface of the earth.

The following notations will be used hereinafter:

O, center of the earth;

Ro, radius of the earth;

l, the non-GSO satellite positioned at latitude l and orbit height h';

G, the GSO satellite positioned at longitude L, latitude Δl and orbitheight h wherein longitude is measured relative to the non-GSOsatellite;

lo, the point of latitude 0 and relative longitude 0 at the same heightas l; and

M, the instantaneous location of the ground station on the surface ofthe earth.

A first reference frame in FIG. 6 defined relative to the position ofthe non-GSO satellite may be characterized as follows:

lz is a vector directed from the non-GSO satellite to the center of theearth;

ly is a vector in the longitude plane containing l, is directedperpendicular to lz, and points in the north direction; and

lx is oriented such that lxyz is orthonormal.

A second frame of reference is denoted as loXYZ, and is similar to thereference frame lxyz but uses lo rather than l as an origin. Thereference frame lxyz may be obtained by rotating the reference frameloXYZ through an angle l with respect to the axis OX. The notations usedwithin the second reference frame of FIG. 6 are: ##EQU9##

The spherical coordinates of M in lxyz are (r, θ, φ) so that itscartesian coordinates in lxyz are (r sinθ cosφ, r sinθ sinφ,r cosθ). Apair of directions of interest are given by the following unit vectors:##EQU10## Determination of Forbidden Directions of Transmission from thenon-GSO Satellite

In a preferred approach the forbidden transmission directions from thenon-GSO satellite are calculated with respect to a set of orbitlocations within the geostationary band, i.e., potential positions ofthe GSO satellite. The forbidden directions derived with respect to eachGSO satellite position may be envisioned as forming a beam, originatingat the non-GSO satellite, the edges of which illuminate points on theearth's surface from which the topocentric angles between the non-GSOsatellite and the associated GSO satellite are equal to the minimumdiscrimination angle D_(min). The following section describes a methodfor determining the shape of the forbidden beam in terms of a set ofunit vectors v, wherein each value of v specifies a linear path betweenthe non-GSO satellite and a location on the surface of the earth. Inthis way the contour of the forbidden band of locations on the surfaceof the earth may be determined with knowledge of the shape of theforbidden beam.

Referring to FIG. 6, the coordinates of the satellite G may be expressedin terms of the non-GSO satellite reference lxyz as follows: ##EQU11##so that: ##EQU12##

By calculating the scalar square of equation (18), one obtains:##EQU13##

The range r between a ground station location and the non-GSO satellitemay be expressed as: ##EQU14##

Furthermore, ##EQU15## leads to: ##EQU16##

Combining equations (19), (20) and (22), one thus has u.v in function ofθ. The two unit vectors given by equation (16) may also be representedin the xyz reference as follows: ##EQU17## so that: ##EQU18##

Combined with the other expression of u.v given in equation (22),equation (24) leads to a relation between θ and φ, which can be written:

    A(θ) cos φ+B(θ) sin φ=C(θ)       (25)

This results in 0, 1 or 2 values of θ for a given value of φ. For asolution (θ, φ) of the equation, the corresponding unit vector vcorresponds to the direction of a ray on the periphery of the "forbiddenbeam", i.e., the beam defined by the values of l, L, Δl and η. Thecalculation of φ values corresponding to a sufficient number of θ valuesthus yields an approximation of the contour of the forbidden beam underconsideration. Superposition of a sufficient number of forbidden beams,with each forbidden beam corresponding to a particular GSO satellitelocation, enables determination of the forbidden band of locations onthe surface of the earth associated with the location of the non-GSOsatellite. In a particular implementation the GSO satellite locationsconsidered are at specified values of allowed GSO satellite driftlatitude (e.g., +3 and -3 degrees). At each drift latitude calculationsare performed from a plurality of longitudes relative to the longitudeof the non-GSO satellite.

Representation of the Forbidden Band in the Non-GSO Satellite Reference

Referring to FIG. 6, each direction from the non-GSO satellite l isrepresented by the projection in plane lxy of the corresponding unitvector. Each forbidden direction, defined by a value of θ and a value ofφ, is thus represented in a plane by a point of cartesian coordinates(x=sinθ cosφ, y=sinθ sinφ). In this representation format the field ofview of the non-GSO satellite is circular.

It is noted that this representation format differs from a satellitereference in which azimuth and elevation are specified. In these tworepresentations the directions from the satellite are related by:##EQU19## and are thus coincident when small angles are involved. Inazimuth/elevation representation, the field of view of the satellitewill not be circular unless both the azimuth and the elevation anglesare small.

An exact representation of the forbidden band requires consideration ofthe forbidden beams corresponding to all positions within thegeostationary band within view of the non-GSO satellite underconsideration. Nonetheless, in particular implementations it may besufficient to approximate this exact representation by a horizontallatitude band encompassing all points within the exact representation.This approximation may be defined in terms of two values of elevationwithin the field of view of the non-GSO satellite. Moreover, thishorizontal approximation of the forbidden band allows a straightforwardrealization of the antenna 132 (FIG. 5) of the non-GSO satellite as aconventional linear feed array.

Referring to FIG. 7a, an exact representation and an approximation of aforbidden band are shown within the field of view (FOV) of anon-geostationary satellite. In particular, the exact forbidden band isshown as the cross-hatched region between the dashed lines while thehorizontal approximation is defined by the elevations E1 and E2. Theparticular example of FIG. 7a corresponds to the situation in which thenon-GSO satellite is in orbit at an altitude of 1800 km at a latitude of25 degrees, and in which the minimum discrimination angle required foracceptable interference is 7 degrees. This results in a forbidden bandapproximation in which the elevations E1 and E2 are at 10.1 degrees and41.8 degrees, respectively, relative to the center C1 of the non-GSOfield of view.

An additional example of a projection of the forbidden band within thefield of view of a non-GSO satellite at an altitude of 1800 km at alatitude of 10 degress is provided by FIG. 7b. Specifically, forbiddentbands are shown for minimum discrimination angles of 3 degress (solidline), 5 degrees (dashed line), and 7 degrees (dotted line). In therepresentation of FIG. 3 the forbidden bands correspond to orthographic(sine) projections mapped according to the function sin(θ), where θdenotes latitude.

Representation of Forbidden Band on Surface of Earth

In this section the forbidden band within the non-GSO satellitereference depicted in FIG. 7a will be transformed to a correspondingforbidden band on the surface of the earth. The transformation entailscalculation of the longitude L_(M) and latitude l_(M) (with respect tothe non-GSO satellite position) of the point M on the earth's surfacecorresponding to a given direction from the non-GSO satellite. Thiscalculation requires finding an xyz coordinate representation of thevector OM based on the following expression: ##EQU20##

The values of l_(M) and L_(M) are then simply derived as functions of θand φ. This transformation from (θ,φ) to (L_(M),l_(M)) allows theintersection with the earth's surface of any ray from the non-GSOsatellite to be represented in terms of longitude and latitude upon anearth map. The transformation is initiated by considering (i) therepresentation of the field of view of the non-GSO satellite: ##EQU21##and, (ii) the two values of elevation (EI) within the non-GSO referenceframe associated with the boundaries of the horizontal approximation ofthe forbidden band. The following expression holds at each boundaryelevation El:

    sin θ sin φ=sin El                               (29)

Referring to FIG. 8a, there is shown a representation on the earth'ssurface of the horizontal forbidden band of FIG. 7a. Specifically, thefield of view of the non-GSO satellite is denoted in FIG. 8a by thesolid line FOV', while the limits of the approximation of the forbiddenband are indicated by the dashed line E1' and E2'. It is noted that thehorizontal limits E1 and E2 of the forbidden band within the non-GSOsatellite reference are transformed to the curved segments E1' and E2'on the earth's surface.

As an additional example, FIG. 8b shows projections upon the earth'ssurface of a set of forbidden bands (solid lines) together with theprojections of the associated fields of view (dashed lines). Theprojections correspond to a plurality of latitude positions of a non-GSOsatellite in orbit at an altitude of 1800 km, and assume a minimumdiscrimination angle of 7 degrees. The relative longitudinal positionsof the forbidden bands were varied in order to minimize mutualsuperposition.

Alternative Implementations,

Referring again to FIG. 5, in other embodiments of the antenna controlsystem 100 the boundaries of the forbidden band could be determined inreal-time rather than using a look-up table 116. For example, latitudeand longitude information from the position acquisition subsystem 120(FIG. 5) could be used by a microprocessor or the like on-board thenon-geostationary satellite to determine the shape of the forbidden bandin accordance with the analytical expressions set forth in the aboveequations. In another implementation such real-time calculations wouldbe performed at a ground station and transmitted to thenon-geostationary satellite. In each of these implementations thecontrol system 100 would then operate as described above to project anantenna beam only to those regions outside of the forbidden band.

While the present invention has been described with reference to a fewspecific embodiments, the description is illustrative of the inventionand is not to be construed as limiting the invention. Variousmodifications may occur to those skilled in the art without departingfrom the true spirit and scope of the invention as defined by theappended claims.

What is claimed is:
 1. A method of operation of a satellite systemhaving a geostationary orbital band occupied by at least onegeostationary satellite and a non-geostationary satellite in an orbit ata lower altitude than that of said at least one geostationary satellite,comprising the steps of:determining position of said non-geostationarysatellite relative to the surface of the earth; calculating a minimumdiscrimination angle between said geostationary band andnon-geostationary satellite at its determined position relative to aground station on earth, wherein said minimum discrimination anglecorresponds to a predefined threshold of interference between signalsreceived by said ground station from said non-geostationary satelliteand geostationary satellites in said geostationary orbital band;defining a forbidden band of locations on the surface of the earth fromwhich said geostationary orbital band and said non-geostationarysatellite, at its determined position, are separated by less than saidminimum discrimination angle; and controlling transmission of signalenergy from said non-geostationary satellite in accordance with saidposition thereof so as to prevent transmission of signal energy fromsaid non-geostationary satellite to said locations within said forbiddenband.
 2. The method of operation of claim 1 wherein said step ofcontrolling transmission further includes the step of adjusting anantenna beam pattern projected by said non-geostationary satellite suchthat energy therefrom is not incident upon said locations within saidforbidden band.
 3. The method of operation of claim 2 wherein said stepof adjusting said antenna beam pattern further includes the step ofprojecting spot beams only to regions on the surface of the earthoutside of said forbidden band of locations.
 4. The method of operationof claim 1 wherein said step of defining a forbidden band of locationson the surface of the earth includes the step of specifying a forbiddenband of latitude range on the surface of the earth from within whichselected orbital positions proximate said geostationary orbit areseparated from said non-geostationary satellite by less than saidminimum discrimination angle.
 5. The method of operation of claim 1wherein said step of controlling transmission includes the step ofpreventing transmission of signals from said non-geostationary satellitewithin a field of view thereof encompassing said forbidden band.
 6. Themethod of operation of claim 1 wherein said step of defining a forbiddenband of locations on the surface of the earth includes the step ofstoring forbidden bands of locations corresponding to selected positionsof said non-geostationary satellite in a memory on saidnon-geostationary satellite.
 7. The method of operation of claim 6wherein said step of controlling transmission of signal energy from saidnon-geostationary satellite includes the step of preventing transmissionof signal energy from said non-geostationary satellite to said forbiddenbands of locations stored in said memory in accordance with saiddetermined position of said non-geostationary satellite.
 8. A satellitesystem having a geostationary orbital band occupied by at least onegeostationary satellite and a non-geostationary satellite in an orbit ata lower altitude than that of said at least one geostationary satellite,said non-geostationary satellite including an antenna control subsystemcomprising:position acquisition means for determining position of saidnon-geostationary satellite relative to the surface of the earth; a dataprocessor, coupled to said position acquisition means, that defines aforbidden band of locations on the surface of the earth from which saidgeostationary orbital band and said non-geostationary satellite, at itsdetermined position, are separated by less than a specified minimumdiscrimination angle; and means, coupled to said data processor, forcontrolling transmission of signal energy from said non-geostationarysatellite in accordance with said position thereof so as to preventtransmission of signal energy from said non-geostationary satellite tosaid locations within said forbidden band.
 9. The system of claim 8wherein said means for controlling transmission further includes meansfor adjusting an antenna beam pattern projected by said second satellitesuch that energy therefrom is not incident upon said locations withinsaid forbidden band.
 10. The system of claim 9 wherein said means foradjusting said antenna beam pattern further includes means forprojecting spot beams only to regions on the surface of the earthoutside of said forbidden band of locations.
 11. The system of claim 8wherein said data processor includes means for specifying a forbiddenband of latitude range on the surface of the earth from within whichselected orbital positions proximate said geostationary orbit areseparated from said second satellite by less than said minimumdiscrimination angle.
 12. The system of claim 8 wherein said means forcontrolling transmission includes means for preventing transmission ofsignals from said second satellite within a field of view thereofencompassing said forbidden band.
 13. The system of claim 8 wherein saiddata processor further includes a memory that stores forbidden bands oflocations corresponding to selected positions of said non-geostationarysatellite in a memory on said non-geostationary satellite.
 14. Thesystem of claim 13 wherein said means for controlling transmission ofsignal energy from said non-geostationary satellite includes means forpreventing transmission of signal energy from said non-geostationarysatellite to said forbidden bands of locations stored in said memory inaccordance with said determined position of said non-geostationarysatellite.
 15. A method of operation of a satellite system having ageostationary orbital band occupied by at least one geostationarysatellite and a non-geostationary satellite in an orbit at a loweraltitude than that of said at least one geostationary satellite,comprising the steps of:determining position of said non-geostationarysatellite relative to the surface of the earth; defining a forbiddenband of locations on the surface of the earth from which saidgeostationary orbital band and said non-geostationary satellite, at itsdetermined position, are separated by less than a specified minimumdiscrimination angle corresponding to a predefined threshold ofinterference at the surface of the earth between signals from saidnon-geostationary satellite and said geostationary satellites in saidgeostationary orbital band; and controlling transmission of signalenergy from said non-geostationary satellite in accordance with saidposition thereof so as to prevent transmission of signal energy fromsaid non-geostationary satellite to said locations within said forbiddenband.
 16. The method of operation of claim 15 wherein said step ofcontrolling transmission further includes the step of adjusting anantenna beam pattern projected by said non-geostationary satellite suchthat energy therefrom is not incident upon said locations within saidforbidden band.
 17. The method of operation of claim 16 wherein saidstep of adjusting said antenna beam pattern further includes the step ofprojecting spot beams only to regions on the surface of the earthoutside of said forbidden band of locations.
 18. The method of operationof claim 15 wherein said step of defining a forbidden band of locationson the surface of the earth includes the step of storing forbidden bandsof locations corresponding to selected positions of saidnon-geostationary satellite in a memory on said non-geostationarysatellite.
 19. The method of operation of claim 18 wherein said step ofcontrolling transmission of signal energy from said non-geostationarysatellite includes the step of preventing transmission of signal energyfrom said non-geostationary satellite to said forbidden bands oflocations stored in said memory in accordance with said determinedposition of said non-geostationary satellite.